Related papers: Small worlds
Small world models are networks consisting of many local links and fewer long range 'shortcuts', used to model networks with a high degree of local clustering but relatively small diameter. Here, we concern ourselves with the distribution…
The small-world network model is a simple model of the structure of social networks, which simultaneously possesses characteristics of both regular lattices and random graphs. The model consists of a one-dimensional lattice with a low…
We explore a new variant of Small-World Networks (SWNs), in which an additional parameter ($r$) sets the length scale over which shortcuts are uniformly distributed. When $r=0$ we have an ordered network, whereas $r=1$ corresponds to the…
Efficiency in passage times is an important issue in designing networks, such as transportation or computer networks. The small-world networks have structures that yield high efficiency, while keeping the network highly clustered. We show…
We introduce and define three types of small worlds: small worlds based on the diameter of the network (SWD), those based on the average geodesic distance between nodes (SWA), and those based on the median geodesic distance (SWMd). These…
We investigate the effect of directed short and long range connections in a simple model of small world network. Our model is such that we can determine many quantities of interest by an exact analytical method. We calculate the function…
In this study, the concept of small worlds is investigated in the context of large-scale wireless ad hoc and sensor networks. Wireless networks are spatial graphs that are usually much more clustered than random networks and have much…
Many real life networks, such as the World Wide Web, transportation systems, biological or social networks, achieve both a strong local clustering (nodes have many mutual neighbors) and a small diameter (maximum distance between any two…
Small-world networks provide an interesting framework for studying the interplay between regular and random graphs, where links are located in a regular and random way, respectively. On one hand, the random links make the model to obey some…
Small-world networks are highly clustered networks with small distances among the nodes. There are many biological neural networks that present this kind of connections. There are no special weightings in the connections of most existing…
We investigate small-world networks from the point of view of their origin. While the characteristics of small-world networks are now fairly well understood, there is as yet no work on what drives the emergence of such a network…
It is commonly known that there exist short paths between vertices in a network showing the small-world effect. Yet vertices, for example, the individuals living in society, usually are not able to find the shortest paths, due to the very…
We investigate a relationship network of humans located in a metric space where relationships are drawn according to a distance-dependent probability density. The obtained spatial graph allows us to calculate the average separation of…
Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…
Networks with underlying metric spaces attract increasing research attention in network science, statistical physics, applied mathematics, computer science, sociology, and other fields. This attention is further amplified by the current…
A model for the spread of an infection is analyzed for different population structures. The interactions within the population are described by small world networks, ranging from ordered lattices to random graphs. For the more ordered…
Most real-world networks are endowed with the small-world property, by means of which the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. The evidence sparkled a wealth of studies…
The mathematical study of the small-world concept has fostered quite some interest, showing that small-world features can be identified for some abstract classes of networks. However, passing to real complex systems, as for instance…
The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order. Next, we introduce a new class of small…
Quantitative descriptions of network structure in big data can provide fundamental insights into the function of interconnected complex systems. Small-world structure, commonly diagnosed by high local clustering yet short average path…